A Novel Thermal Tactile Sensor Based on Micro Thermoelectric Generator for Underwater Flow Direction Perception

Underwater vehicles can operate independently in the exploitation of marine resources. However, water flow disturbance is one of the challenges underwater vehicles must face. The underwater flow direction sensing method is a feasible way to overcome the challenges but faces difficulties such as integrating the existing sensors with underwater vehicles and high-cost maintenance fees. In this research, an underwater flow direction sensing method based on the thermal tactility of the micro thermoelectric generator (MTEG) is proposed, with the theoretical model established. To verify the model, a flow direction sensing prototype is fabricated to carry out experiments under three typical working conditions. The three typical flow direction conditions are: condition No. 1, in which the flow direction is parallel to the x-axis; condition No. 2, in which the flow direction is at an angle of 45° to the x-axis; and condition No. 3, which is a variable flow direction condition based on condition No. 1 and condition No. 2. According to the experimental data, the variations and orders of the prototype output voltages under three conditions fit the theoretical model, which means the prototype can identify the flow direction of three conditions. Besides, experimental data show that in the flow velocity range of 0~5 m/s and the flow direction variation range of 0~90°, the prototype can accurately identify the flow direction in 0~2 s. The first time utilizing MTEG on underwater flow direction perception, the underwater flow direction sensing method proposed in this research is cheaper and easier to be applied on the underwater vehicles than traditional underwater flow direction sensing methods, which means it has great application prospects in underwater vehicles. Besides, the MTEG can utilize the waste heat of the underwater vehicle battery as the energy source to achieve self-powered work, which greatly enhances its practical value.


Introduction
The Remote Operated Vehicle (ROV) and Autonomous Underwater Vehicle (AUV) are underwater vehicles often utilized in underwater operations such as seabed topography surveys, underwater rescue and salvage, and marine pasture farming [1]. The performance of ROV and AUV is affected by many factors. For example, the cable affects the movement distance of ROV [2], battery power affects the endurance time of AUV, and data transmission affects the work efficiency of the AUV [3]. However, water flow disturbance, which includes the impact of high-velocity water flow and the disturbance of a vortex, is a challenge ROV and AUV both face [4].
The underwater environment is out of the ordinary. Besides high water pressure and low visibility, unpredictable strong current disturbances may lead to ROV and AUV losing balance and orientation. For ROV, losing balance may cause the cables to wrap around for current meters, which makes the installation of current meters difficult. Some current meters are expensive, causing a high installation cost. Another challenge is adaptability. The assumed carrier of the current meters is not the underwater vehicle. Therefore, the consumed power of the current meters may be a heavy burden for underwater vehicles, which may lead the performance of underwater vehicles to degrade.
Recently, ADV and ADCP have been utilized in the estimation of ocean turbulence [19] and observation of ocean current structure [20], which means ADV and ADCP have made outstanding contributions to the exploration of the ocean. However, the ADV and ADCP are also difficult to be applied to underwater vehicles. As for the mechanical current meter and electromagnetic current meter, their research has almost stopped in recent years owing to their disadvantages.
Traditional current meters generally have problems such as high cost, high energy consumption, and high difficulty in integrating into underwater vehicles, which need a long time to be solved. Due to the previous research of our team on the micro thermoelectric generator (MTEG) [21][22][23][24], we intend to propose an underwater flow direction sensing method based on MTEG to solve those problems. During this process, the microelectron mechanical systems (MEMS) thermal flow sensor has inspired us. Compared with traditional flow sensors, MEMS thermal flow sensors are manufactured by microelectronics and micromachining technology and have the advantages of small size, light weight, low cost, low power consumption, high reliability, being suitable for mass production, and ease of integration [25]. At the same time, the processing of the micron level makes it possible for MEMS thermal flow sensors to perform some special functions which traditional flow sensors cannot achieve. The MEMS thermal flow sensor identifies the flow velocity by monitoring the heat transfer, which has the advantages of high sensitivity, high accuracy, and small output signal drift [26]. Though the MEMS thermal flow sensor has many merits, it cannot be directly applied in underwater scenarios. The main reason is that the sophisticated circuitry of the MEMS thermal flow sensor can be easily corroded by water, even after some waterproof treatments. Once the circuitry is corroded, the MEMS thermal flow sensor is almost impossible to work normally. Based on the MEMS thermal flow sensor, the thermal tactile underwater flow sensing sensor proposed in this paper has the advantages of small size, light weight, low cost and ease of integration compared with traditional current meters. Besides, compared with the MEMS thermal flow sensor, the circuitry of the thermal tactile underwater flow sensing sensor does not directly contact with water, which means the circuitry is less likely to be corroded by water. Most importantly, due to the thermoelectric effect of MTEG, the thermal tactile underwater flow sensing sensor can realize self-powered work, which greatly increases its application value. Figure 1a shows the underwater flow direction prototype installed in a manipulator, and the structure of the flow direction prototype is shown in Figure 1b. The prototype consists of the thermal tactile unit insulation layer, the thermal tactile unit, the heat source, the heat source insulation layer, and the prototype shell. Among them, the function of the thermal tactile unit insulation layer and the heat source insulation layer is to keep the thermal tactile unit and the heat source insulated from the shell. The thermal tactile unit, which is the core of the prototype, converts the temperature difference between the cold end, which is close to the thermal tactile unit insulation layer, and the hot end, which is close to the heat source, into the prototype output voltage. The working principle of the thermal tactile unit is the Seebeck effect, which is shown in Figure 1c. Both ends of the P-type and N-type semiconductors are in contact with a high temperature, corresponding to the hot end, and a low temperature, corresponding to the cold end, respectively. Due to the temperature difference between the hot and cold ends, the holes in the P-type semiconductor and the electrons in the N-type semiconductor move from the hot end to the cold end. Therefore, a voltage is generated between the two ends, and the voltage is proportional to the temperature difference. The thermoelectric materials utilized in the thermal tactile unit were fabricated by our team [21], and the output voltage of the thermal tactile unit increases 0.072 V with a 1 K temperature increase, as shown in Figure 1d. The function of the heat source is to keep the hot end of the thermal tactile unit at a stable temperature. In application, the parts with high heat dissipation, such as the battery of underwater vehicles, can be utilized as the heat source. P−type and N−type semiconductors are in contact with a high temperature, corresponding to the hot end, and a low temperature, corresponding to the cold end, respectively. Due to the temperature difference between the hot and cold ends, the holes in the P−type semiconductor and the electrons in the N−type semiconductor move from the hot end to the cold end. Therefore, a voltage is generated between the two ends, and the voltage is proportional to the temperature difference. The thermoelectric materials utilized in the thermal tactile unit were fabricated by our team [21], and the output voltage of the thermal tactile unit increases 0.072 V with a 1 K temperature increase, as shown in Figure 1d. The function of the heat source is to keep the hot end of the thermal tactile unit at a stable temperature. In application, the parts with high heat dissipation, such as the battery of underwater vehicles, can be utilized as the heat source. Due to the insulating effect of the insulation layers, only the cold end of the thermal tactile unit can exchange heat with the prototype shell. Besides, since the cold end partially protrudes from the prototype shell, the cold end can exchange heat with the water, which is the premise that the prototype can identify the flow direction.

Theoretical Model
As shown in Figure 2a, a three−dimensional coordinate system is established and the flow direction sensing method can identify any flow direction of the water in the . The flow direction sensor can collect flow velocity data and accurately identify the flow direction. When performing control algorithms, the flow direction and velocity data can make the underwater vehicle or manipulator better cope with the complex underwater environment. Therefore, the difficulty of stabilizing the attitude of the underwater vehicle or manipulator is reduced, and the efficiency and safety of the underwater vehicle when performing the area detection task are improved. Due to the insulating effect of the insulation layers, only the cold end of the thermal tactile unit can exchange heat with the prototype shell. Besides, since the cold end partially protrudes from the prototype shell, the cold end can exchange heat with the water, which is the premise that the prototype can identify the flow direction.
As shown in Figure 2a, a three-dimensional coordinate system xyz is established and the flow direction sensing method can identify any flow direction of the water in the xyz. The flow direction sensor can collect flow velocity data and accurately identify the flow direction. When performing control algorithms, the flow direction and velocity data can make the underwater vehicle or manipulator better cope with the complex underwater environment. Therefore, the difficulty of stabilizing the attitude of the underwater vehicle or manipulator is reduced, and the efficiency and safety of the underwater vehicle when performing the area detection task are improved.
The manipulator is the main tool of the underwater vehicle when performing tasks, but the small volume and low weight of the manipulator make it more difficult to deal with the water flow disturbance. At the same time, the volume of the manipulator also makes it more difficult to apply the traditional current meters, which means it needs a new current meter more urgently than the underwater vehicle. Therefore, the research selects the manipulator to verify the feasibility of the flow direction sensing method based on the thermal tactility of MTEG. For the manipulator, the most important factor in the attitude stability and motion of the manipulator is the vertical water flow, as shown by the red arrows in Figure 2a. Therefore, the vertical flow of the manipulator is selected to verify the flow direction sensing method. Thus, the coordinate system xoz is established on the plane where the four thermal tactile sensors D1, D2, D3, and D4 are located, as shown in The manipulator is the main tool of the underwater vehicle when performing tasks, but the small volume and low weight of the manipulator make it more difficult to deal with the water flow disturbance. At the same time, the volume of the manipulator also makes it more difficult to apply the traditional current meters, which means it needs a new current meter more urgently than the underwater vehicle. Therefore, the research selects the manipulator to verify the feasibility of the flow direction sensing method based on the thermal tactility of MTEG. For the manipulator, the most important factor in the attitude stability and motion of the manipulator is the vertical water flow, as shown by the red arrows in Figure 2a. Therefore, the vertical flow of the manipulator is selected to verify the flow direction sensing method. Thus, the coordinate system is established on the plane where the four thermal tactile sensors 1, 2, 3, and 4 are located, as shown in Figure 2b. The x−axis is parallel to the line between 2 and 4, and the x−axis is parallel to the line between 1 and 3.
The core of the thermal tactile sensor is MTEG. According to the principle of MTEG, the faster the water flow velocity, the greater the temperature difference between the cold end and the hot end of MTEG. Finally, the output voltage of MTEG increases. The relationship between the output voltage of MTEG and the water flow velocity is derived in detail in the Supporting Information, and here, we only give the relationship: The core of the thermal tactile sensor is MTEG. According to the principle of MTEG, the faster the water flow velocity, the greater the temperature difference between the cold end and the hot end of MTEG. Finally, the output voltage of MTEG increases. The relationship between the output voltage of MTEG and the water flow velocity is derived in detail in the Supporting Information, and here, we only give the relationship: V is the output voltage of METG, k 1 and k 2 are constants defined by the characteristics of MTEG, and u is the flow velocity of the water which flows through MTEG. Generally, the flow velocity of the water which flows through MTEG is the flow velocity of the water which flows through the thermal tactile sensor.
The realization of flow direction perception is based on Equation (1). The operating conditions analyzed in this paper are shown in Figure 2a(II), in which water flows at a speed u 0 through a plane composed of four sensor devices at an angle α to the x-axis. The analysis of water flow through a plate is one of the research hotspots in the field of hydrodynamics, which usually includes the analysis of flow pressure, flow Sensors 2023, 23, 5375 6 of 14 velocity, flow rate, and other parameters. Some researchers choose to simplify the flow field by the vector decomposition method in the flow velocity analysis so that they can focus on the analysis and calculation of the flow velocity [27][28][29]. Since the water flow velocity directly affects the output performance of MTEG, the flow velocity sensing is an important factor affecting the conclusion of the flow direction sensing method proposed in this paper. Therefore, based on the relevant research conclusions, the vector decomposition method is also adopted to simplify the flow field analysis in this research.
Ideally, the water flow can be decomposed into u 1 , which is parallel to the x-axis, and u 4 , which is parallel to the x-axis. The u 1 flows through D1, and the u 4 flows through D4. The velocity of the u 1 and u 4 can be calculated by the following equations: Therefore, α can be calculated by the following equation: Combining Equation (1) and Equation (4), α can also be calculated by the following equation: Because D1 is symmetrical with D3, D2 is symmetrical with D4, and 90 ≥ α ≥ 0; the velocity of u 2 , which flows through D2, is less than the velocity of u 4 , and the velocity of u 3 , which flows through D3, is less than the velocity of u 1 . The output voltages of different thermal tactile sensors can be obtained by Equation (1). By comparing the output voltages of four thermal tactile sensors, the water flow at an angle of α can be identified.
The study simulates the flow of two typical angles, as shown in Figure 2c. In Figure 2c(I), u 1 ≈ u 3 ≈ 5 m/s, which is consistent with the theoretical model but different from the theoretical model, u 2 = 0, u 4 = 0. This is because the velocity of the water flow cannot be zeroed due to the existence of obstacles, so the velocity of u 2 is not the same as 0 derived from the theoretical model. However, u 4 ≤ u 2 is still consistent with the theoretical model. Therefore, V D1 = V D3 > V D2 > V D4 ; the water flow direction can be identified by comparing the output voltages of four thermal tactile sensors.
In Figure 2c(II), The simulation of water flow is consistent with the derivation of the theoretical model. Therefore, V D2 = V D3 > V D4 = V D1 , the water flow direction can be identified by comparing the output voltages of four thermal tactile sensors.
It can be seen from Figure 2c that the simulation of water flow is consistent with the theoretical model except for rare special angles. Although the simulation is not consistent with the theoretical model at those special angles, it does not affect the perception of the flow direction. For ease of comparison, the matrices A and B are set as follows: The results of matrices comparison and flow direction are shown in Table 1.

Experimental System
In order to verify the theoretical model and test the performance of the underwater flow direction sensing prototype, a flow direction sensing experimental system is designed, as shown in Figure 3.      Figure 1b. In experiment, the input power of a temperature control unit is in the range 2~3 W. The thermal tactile units transform the heat exchange between the thermal tactile unit and the environment into voltage to identify the flow direction of the water, which corresponds to 2 in Figure 1b. The dimension of the thermal tactile unit is 9 × 11 × 8 mm 3 and the dimension of the prototype is 50 × 50 × 34 mm 3 .
The prototype is connected with the temperature sensing unit shown in Figure 3f and the voltage acquisition unit shown in Figure 3g. The temperature sensing unit is utilized to monitor the temperature of the heat source in real time. The voltage acquisition unit is utilized to collect the prototype output voltage and input it to the data processing terminal shown in Figure 3e in real time. During the experiment, the water flow velocity is adjusted by adjusting the rotational speed of the centrifugal pump shown in Figure 3i and monitored by the electromagnetic flowmeter shown in Figure 3h. The direction of the flow is manually adjusted with an elongated plastic hose to flow over the prototype. Once the flow velocity or flow direction is changed, the voltage acquisition unit records the output voltage of the prototype and input the voltage data to the data processing terminal.
Three typical flow direction conditions are set up to verify the performance of the prototype. They are condition No. 1, in which the flow direction is parallel to the x-axis, and condition No. 2, in which the flow direction is at an angle of 45 • to the x-axis. As for condition No. 3, it is a variable flow direction condition based on condition No. 1 and condition No. 2. In the three conditions, the hot end temperature of the thermal tactile units is set at 313 K, which is the normal working temperature of the lithium battery pack utilized in the underwater vehicle [30]. Besides, the water temperature is 293 K, which is the surface temperature of the sea in summer [31]. Therefore, the initial temperature difference of the thermal tactile units is 20 K.   As shown in Figure 4e, the flow direction is controlled to be parallel to the x−axis. The velocity of the flow is set at 1 m/s, 3 m/s, and 5 m/s to verify whether the prototype can identify the flow direction at different velocities.

When the Flow Direction Is at an Angle of 45° to the x−axis (Condition No. 2)
As shown in Figure 5e, the flow direction is controlled to be at an angle of 45° to the x−axis. The velocity of flow is set at 1 m/s, 3 m/s, and 5 m/s.

Variable Flow Direction Condition (Condition No. 3)
As shown in Figure 6e, the flow is controlled parallel to the x-axis. In 0~3 s, the prototype keeps still. In 3~4 s, the prototype rotates 45 • at a speed of 45 • /s. In 4~5 s, the prototype keeps still. In 5~6 s, the prototype rotates 45 • at a speed of 45 • /s. In 6~7 s, the prototype keeps still. The velocity of flow is set at 1 m/s, 3 m/s, and 5 m/s.   Figure 6f is the output voltage of four thermal tactile sensors for flow direction meas- Obviously, the order is in accord with the theoretical model, which means that the prototype can correctly identify the variable flow direction under condition No. 3. Figure 6f is the output voltage of four thermal tactile sensors for flow direction measurement in a full range of 90 • at 5 m/s. As shown in Figure 6f, within the water flow angle of 0~90 • , the voltage curve of D1 is similar to the voltage curve of D4, and the voltage curve of D2 is similar to the voltage curve of D3. According to Figure 6f, the voltage variations of four thermal tactile sensors are regular, which means it is feasible for the prototype to identify the water flow from 0 • to 90 • .
The underwater thermal tactile direction sensing prototype needs to be further optimized, but it still has some merits compared to the traditional current meters and MEMS thermal flow sensor. The comparisons are shown in the Table 2. For a more detailed comparison of data, such as price, accuracy, dimension, etc., please refer to Table S1 of the Supporting Information. of 0~90°, the voltage curve of 1 is similar to the voltage curve of 4, and the voltage curve of 2 is similar to the voltage curve of 3. According to Figure 6f, the voltage variations of four thermal tactile sensors are regular, which means it is feasible for the prototype to identify the water flow from 0° to 90°. The underwater thermal tactile direction sensing prototype needs to be further optimized, but it still has some merits compared to the traditional current meters and MEMS thermal flow sensor. The comparisons are shown in the Table 2. For a more detailed comparison of data, such as price, accuracy, dimension, etc., please refer to Table S1 of the Supporting Information.

Implications and Prospects
This research studies whether the flow direction sensing prototype based on the flow direction sensing method can successfully realize the direction perception at some angles. Although the three conditions in this paper can represent any flow direction in the whole two−dimensional coordinate system, more experimental data are still necessary to support it. Therefore, in the future, we need to perform experiments on the entire two−dimensional coordinate system. In fact, we have already tested the flow direction sensing prototype when the flow direction is at an angle of 15°, 30°, 60°, 75°, 90° to the x−axis and put the data in the Supporting Information, but we know those data are far from enough. Besides, if we want to make the flow direction sensing prototype better applied in practice, we need to study whether it can realize direction perception in a three−dimensional coordinate system. In order to identify the flow direction in the three−dimensional coordinate system, the prototype and the theoretical model in this research need to be updated. In summary, there are much work to do in the future.

Mechanical transmission
Easy to be manufactured and maintained Easy to be influenced by water flow disturbance Electromagnetic Current Meter x FOR PEER REVIEW 12 of 15 of 0~90°, the voltage curve of 1 is similar to the voltage curve of 4, and the voltage curve of 2 is similar to the voltage curve of 3. According to Figure 6f, the voltage variations of four thermal tactile sensors are regular, which means it is feasible for the prototype to identify the water flow from 0° to 90°. The underwater thermal tactile direction sensing prototype needs to be further optimized, but it still has some merits compared to the traditional current meters and MEMS thermal flow sensor. The comparisons are shown in the Table 2. For a more detailed comparison of data, such as price, accuracy, dimension, etc., please refer to Table S1 of the Supporting Information.

Implications and Prospects
This research studies whether the flow direction sensing prototype based on the flow direction sensing method can successfully realize the direction perception at some angles. Although the three conditions in this paper can represent any flow direction in the whole two−dimensional coordinate system, more experimental data are still necessary to support it. Therefore, in the future, we need to perform experiments on the entire two−dimensional coordinate system. In fact, we have already tested the flow direction sensing prototype when the flow direction is at an angle of 15°, 30°, 60°, 75°, 90° to the x−axis and put the data in the Supporting Information, but we know those data are far from enough. Besides, if we want to make the flow direction sensing prototype better applied in practice, we need to study whether it can realize direction perception in a three−dimensional coordinate system. In order to identify the flow direction in the three−dimensional coordinate system, the prototype and the theoretical model in this research need to be updated. In summary, there are much work to do in the future.  Figure 6f, the voltage variations of four thermal tactile sensors are regular, which means it is feasible for the prototype to identify the water flow from 0° to 90°. The underwater thermal tactile direction sensing prototype needs to be further optimized, but it still has some merits compared to the traditional current meters and MEMS thermal flow sensor. The comparisons are shown in the Table 2. For a more detailed comparison of data, such as price, accuracy, dimension, etc., please refer to Table S1 of the Supporting Information.

Implications and Prospects
This research studies whether the flow direction sensing prototype based on the flow direction sensing method can successfully realize the direction perception at some angles. Although the three conditions in this paper can represent any flow direction in the whole two−dimensional coordinate system, more experimental data are still necessary to support it. Therefore, in the future, we need to perform experiments on the entire two−dimensional coordinate system. In fact, we have already tested the flow direction sensing prototype when the flow direction is at an angle of 15°, 30°, 60°, 75°, 90° to the x−axis and put the data in the Supporting Information, but we know those data are far from enough. Besides, if we want to make the flow direction sensing prototype better applied in practice, we need to study whether it can realize direction perception in a three−dimensional coordinate system. In order to identify the flow direction in the three−dimensional coordinate system, the prototype and the theoretical model in this research need to be updated. In summary, there are much work to do in the future.

Doppler principle
High accuracy, wide measuring range Hard to be maintained

MEMS Thermal
Flow Senor x FOR PEER REVIEW 12 of 15 of 0~90°, the voltage curve of 1 is similar to the voltage curve of 4, and the voltage curve of 2 is similar to the voltage curve of 3. According to Figure 6f, the voltage variations of four thermal tactile sensors are regular, which means it is feasible for the prototype to identify the water flow from 0° to 90°. The underwater thermal tactile direction sensing prototype needs to be further optimized, but it still has some merits compared to the traditional current meters and MEMS thermal flow sensor. The comparisons are shown in the Table 2. For a more detailed comparison of data, such as price, accuracy, dimension, etc., please refer to Table S1 of the Supporting Information.

Implications and Prospects
This research studies whether the flow direction sensing prototype based on the flow direction sensing method can successfully realize the direction perception at some angles. Although the three conditions in this paper can represent any flow direction in the whole two−dimensional coordinate system, more experimental data are still necessary to support it. Therefore, in the future, we need to perform experiments on the entire two−dimensional coordinate system. In fact, we have already tested the flow direction sensing prototype when the flow direction is at an angle of 15°, 30°, 60°, 75°, 90° to the x−axis and put the data in the Supporting Information, but we know those data are far from enough. Besides, if we want to make the flow direction sensing prototype better applied in practice, we need to study whether it can realize direction perception in a three−dimensional coordinate system. In order to identify the flow direction in the three−dimensional coordinate system, the prototype and the theoretical model in this research need to be updated. In summary, there are much work to do in the future. of 0~90°, the voltage curve of 1 is similar to the voltage curve of 4, and the voltage curve of 2 is similar to the voltage curve of 3. According to Figure 6f, the voltage variations of four thermal tactile sensors are regular, which means it is feasible for the prototype to identify the water flow from 0° to 90°. The underwater thermal tactile direction sensing prototype needs to be further optimized, but it still has some merits compared to the traditional current meters and MEMS thermal flow sensor. The comparisons are shown in the Table 2. For a more detailed comparison of data, such as price, accuracy, dimension, etc., please refer to Table S1 of the Supporting Information.

Implications and Prospects
This research studies whether the flow direction sensing prototype based on the flow direction sensing method can successfully realize the direction perception at some angles. Although the three conditions in this paper can represent any flow direction in the whole two−dimensional coordinate system, more experimental data are still necessary to support it. Therefore, in the future, we need to perform experiments on the entire two−dimensional coordinate system. In fact, we have already tested the flow direction sensing prototype when the flow direction is at an angle of 15°, 30°, 60°, 75°, 90° to the x−axis and put the data in the Supporting Information, but we know those data are far from enough. Besides, if we want to make the flow direction sensing prototype better applied in practice, we need to study whether it can realize direction perception in a three−dimensional coordinate system. In order to identify the flow direction in the three−dimensional coordinate system, the prototype and the theoretical model in this research need to be updated. In summary, there are much work to do in the future.
Heat conduction, heat convection, and thermoelectric effect Cheap, small volume, easy to be installed and maintained Low accuracy, narrow measuring range

Implications and Prospects
This research studies whether the flow direction sensing prototype based on the flow direction sensing method can successfully realize the direction perception at some angles. Although the three conditions in this paper can represent any flow direction in the whole two-dimensional coordinate system, more experimental data are still necessary to support it. Therefore, in the future, we need to perform experiments on the entire two-dimensional coordinate system. In fact, we have already tested the flow direction sensing prototype when the flow direction is at an angle of 15 • , 30 • , 60 • , 75 • , 90 • to the x-axis and put the data in the Supporting Information, but we know those data are far from enough. Besides, if we want to make the flow direction sensing prototype better applied in practice, we need to study whether it can realize direction perception in a three-dimensional coordinate system. In order to identify the flow direction in the three-dimensional coordinate system, the prototype and the theoretical model in this research need to be updated. In summary, there are much work to do in the future.

Conclusions
An underwater flow direction sensing method based on the thermal tactility of MTEG is proposed, and a theoretical model is established in this research. Based on the theoretical model, a prototype is fabricated to carry out experiments under three typical conditions. The method compares the voltages which are obtained by different thermal tactile sensors of the prototype to identify the flow direction. Under the three typical conditions, the variations and orders of four thermal tactile sensors voltages fit the theoretical model, indicating that the method can identify underwater flow direction. For example, when the flow direction is parallel to the x-axis, the comparison result of water flow velocity through four thermal tactile sensors is u 1 ≈ u 3 > u 2 > u 4 according to the theoretical model. Therefore, the comparison result of voltage should be V D1 ≈ V D3 > V D2 > V D4 . According to Figure 4, the comparison result of the voltages of four thermal tactile sensors is indeed V D1 ≈ V D3 > V D2 > V D4 . It can be seen that the experimental data are consistent with the theoretical model. Besides, according to Figure 4, the voltages of the four thermal tactile sensors can be clearly distinguished since the water flowed over the prototype for 1 s, and the voltages remain stable after 2 s. Therefore, the prototype can identify the flow direction parallel to the x-axis within 2 s. Thus, the prototype can achieve accurate identification in 0~2 s and is not affected by variation of the flow velocity.
Though the accuracy of the prototype is far from those traditional sensors, it is mainly because the prototype requires further circuit design and algorithm optimization. Once the prototype can be further optimized, the accuracy can be greatly improved and may be possible to get close to the traditional sensors. In fact, according to the theoretical model, the accuracy of the thermal tactile sensor can even reach 1 • . Despite the accuracy, the most important merit of the prototype is that it can utilize the battery waste heat as the energy source to achieve self-powered work. Compared with traditional methods, the underwater thermal tactile direction perception proposed in this paper firstly utilizes a micro thermoelectric generator (MTEG) on underwater flow direction perception. MTEG can convert the temperature difference between the underwater vehicle battery and the water into voltage, which means the battery waste heat is converted into electricity by MTEG. Besides, the prototype has merits such as low cost, low operation difficulty, low maintenance difficulty, and so on. Therefore, it not only greatly reduces difficulty and cost in the application of underwater vehicles, but also greatly promotes the application of underwater flow direction sensors in underwater vehicles.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/10 .3390/s23125375/s1, Figure S1. Thermodynamic model of the flow velocity prototype. Figure S2. The marks of the water flow angle. Figure S3. Output voltage of the prototype when the flow direction is 15 • to the x-axis. Figure S4. Output voltage of the prototype when the flow direction is 30 • to the x-axis. Figure S5. Output voltage of the prototype when the flow direction is 60 • to the x-axis. Figure S6. Output voltage of the prototype when the flow direction is 75 • to the x-axis. Figure  S7. Output voltage of the prototype when the flow direction is 90 • to the x-axis. Table S1. The performance comparisons between traditional sensors and the thermal tactile sensor. Video S1. Flow direction experiment video when the flow direction is parallel to the x-axis. Video S2. Flow direction experiment video when the flow direction is at an angle of 45 • to the x-axis. References [23,24,32,33] are cited in the Supplementary Materials.